Are there any vaccines that do not have overwhelmingly positive risk/benefit ratio? (Covid and flu vaccines definitely do!)

The rabies vaccine is not usually used unless the person is at risk. This vaccine can be administered after a bite if the animal is suspected to be infected.

Vaccines made of inactivated (killed) or attenuated (alive, but defective) pathogens are usually more dangerous. Inactivation may not be effective and a virulent pathogen may survive and attenuated pathogens may pick up virulence factors and become fully functional from a different (related) patogen that happes to infect the patient at the same time. Also, when vaccines are prepared from infected animals, manufacturing accidents may happen, such as contamination with something else infectious.

These types of vaccines were mostly replaced by fully synthetic vaccines.

You may read about the old polio vaccine:

https://en.wikipedia.org/wiki/Polio_vaccine